Kolmogorov Complexity in Randomness Extraction

We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a computable function is an almost randomness extractor if and only if it is a Kolmogorov complexityextractor, thus establishing a fundamental equivalence between two forms of extraction studied in the literature: Kolmogorov extractionand randomness extraction. We present a distribution ${\cal M}_k$ based on Kolmogorov complexity that is complete for randomness extraction in the sense that a computable function is an almost randomness extractor if and only if it extracts randomness from ${\cal M}_k$.